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Poster

A unified variance-reduced accelerated gradient method for convex optimization

Guanghui Lan · Zhize Li · Yi Zhou

East Exhibition Hall B + C #153

Keywords: [ Stochastic Methods; ] [ Algorithms -> Large Scale Learning; Algorithms -> Online Learning; Algorithms -> Regression; Algorithms ] [ Optimization ] [ Convex Optimization ]


Abstract:

We propose a novel randomized incremental gradient algorithm, namely, VAriance-Reduced Accelerated Gradient (Varag), for finite-sum optimization. Equipped with a unified step-size policy that adjusts itself to the value of the conditional number, Varag exhibits the unified optimal rates of convergence for solving smooth convex finite-sum problems directly regardless of their strong convexity. Moreover, Varag is the first accelerated randomized incremental gradient method that benefits from the strong convexity of the data-fidelity term to achieve the optimal linear convergence. It also establishes an optimal linear rate of convergence for solving a wide class of problems only satisfying a certain error bound condition rather than strong convexity. Varag can also be extended to solve stochastic finite-sum problems.

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